Performing dilations

perform a dilation on the coordinate plane the dilation should be centered at 9 negative 9 and have a scale factor of 3 so get our dilation tool out will Center it actually I so it's already actually centered at 9 negative 9 we could put this wherever we want but let's Center it at 9 9 negative 9 and we want to scale this up by 3 so one way to think about it just pick any of these points right over here and they're going to have to get three top 3 times further away from our center of dilation so for example this point C right actually let's think about these points where they actually want us to fill something in so point a right over right over here it is it is at the point 4 negative 3 so in the X direction in the X Direction it is 5 it is 5 less than 9 it is 5 less than 9 we want it to be 3 times further than 9 so we want it to be 15 less than 9 so we want the x-coordinate of a 9 minus 15 is negative 6 we want it to go to negative 6 and likewise we want its y-coordinate to be 3 times further so right now let's see it is at negative 3 relative to negative 9 so it is 6 more on the y-direction we want it to be 18 more 18 more the negative 9 would be positive 9 so point a should map to negative 6 comma 9 and that should give us enough information to just make sure that we are dilating up by a factor of 3 so let's see whoops let's dilate up by a factor of 3 so we want to get the image of point a to the point negative 6 comma 9 so we are there there we go we have dilated it up and that we could even look where the point that corresponds to e has map 2 and you can look at each direction it's 3 times further e is now at negative 6 e is at negative 6 comma negative 3 negative 3 the image is of points a and E are 3 times as far as the original points as the original 3 x far apart I should say as the original points and there are three times further from our center of dilation right over you see for example the point E is that has the x coordinate of 4 which is 5 less now it is at negative 6 which is 15 less than our than our center of dilation and the same thing true it's e its y-coordinate is 2 more and now after we mapped it its y-coordinate is 6 more than our center of dilation got it right